Question

Two numbers that multiply to -30 and add to 3?

Answer 1

x+y=3
xy=-30

x+y=3
minusx
y=3-x
sub
x(3-x)=-30
3x-x^2=-30
times -1 both sides
x^2-3x=30
minus 30 both sides
x^2-3x-30=0
use quadratic
for
ax^2+bx+c=0
x=
`(-b+/- √(b^2-4ac) )/(2a)`

1x^2-3x-30=0
a=1
b=-3
c=-30

x=
`(-(-3)+/- √((-3)^2-4(1)(-30)) )/(2(1))`
x=
`(3+/- √(9+120) )/(2)`
x=
`(3+/- √(129) )/(2)`
the numbers are
`(3+ √(129) )/(2)` and
`(3- √(129) )/(2)`